The Field of Logic

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152

THE JOURNAL OF PHILOSOPHY

Once

Twice

4 Times

Duplication
Variation. .
Average. . .
Shryer's. . .

1.00
1.00
1.00
1.00

1.49
2.63
2.06
2.08

2.60
4.05
3.33
3.46

These figures, which are strikingly similar, show a high degree
of correlation between the experimental test of memory and the
practical test of efficiency.

Summary.

1. Increasing size gives a higher memory value than increasing
the number of repetitions of an advertisement when exact dupli-
cates are used.

2. Variation is about twice as effective as duplication.

3. There is a very close correlation between the memory value
of the different forms of presentation of the material and the prac-
tical efficiency of the same forms of presentation in pulling in-
quiries.

Henry F. Adams.
University op Michigan.

THE FIELD OF LOGIC

THE volume of the "Encyclopedia of the Philosophical Sciences"
recently published gives an accurate rehearsal of the present
condition of the science of logic. If there is any direction in the
development of logic it seems to be away from the conception of
that science as a branch of psychology. Among the papers we find
rather less of that peculiar psychology written in terms inherited
from the scholastic logic that characterized the literature under the
head of logic some years ago. The conception of logic as the
science of the empirical process of thought to be dealt with through
the categories of Aristotle or their scholastic modifications for a
time threatened to leave no room for the traditional formal logic
and its modern successor. From this departure logic has been res-
cued by the mathematicians. As a result of the work of Peano and
his followers psychologism has gone out of fashion.

Psychologism has not disappeared from logical writing, however,
and there can be found in the present volume very disconcerting
traces of its survival which threaten a return. The writers of the
volume have approached their task from very different points of
view, but there is one respect in which they are agreed, with vary-

PSYCHOLOGY AND SCIENTIFIC METHODS 153

ing emphasis. Logic is still a science of thought as distinct from
expression. Windleband makes it clear that this does not mean
that in psychology is to be found the ground of logic. "Logic," he
says, "is concerned not with the origin, but with the validity or truth
of ideas. " It is true that this validity is distinguished by means of
a feeling and that it is the task of psychology to establish "the
marks which from a psychological point of view distinguished the
purely theoretical grounds on which perception and knowledge are
accepted from those of opinion and belief," yet, for this thinking
which is directed at truth there are "constraining norms" by which
we proceed from one assertion to another. These norms are not a
matter for the psychologist's investigation. Logic, then, for Windle-
band, applies to thinking which is done under this constraint.
That there exists such thought distinct from any verbal expression
he takes to be proved by instances of aphasia, inability to express
what is in the mind, the fact that mechanical speech is sometimes
accompanied by distinct thought, and, best of all, the fact that we
may have in two different languages the same thought expressed.
Windleband narrowly escapes, if he does escape, the clutches of
the psychologists, who may claim such a thing as a "constraint"
to think thus and so for their own, or may attach the "feeling" by
which a true judgment is distinguished from a false. The other
writers who are given place in the volume are in less danger. Pro-
fessor Royce makes logic a part of a more general science of order
which turns out on examination to be Russell's mathematics. These
forms of order in general "are in fact the forms of all rational ac-
tivity," which is again something different from verbal expression.
For Croce also logic is the science of thought, the thinking proc-
ess as distinguished from expression. It is to include among other
things a theory of error, or the "pathology of thought." From
Couturat we had been led to expect a different attitude. Some
years ago in a discussion with Poincare he offered the suggestion that
logic was not the science of thought, but the body of rules of demon-
stration. We find him in this volume, nevertheless, asserting that
logic is the "normative science of the formal laws of correct think-
ing." It deals with the understanding, not with expression, though
language offers the best example of the operation of the under-
standing. We find practical agreement among the writers of the
volume in these two respects: (1) Thought or meaning is some-
thing competely distinct from and independent of expression. As
Windleband puts it: "... it must, above all, be clearly laid down
that the linguistic relational forms are nothing less than imitations
of the forms of the movement and association of ideas," signs for
these. "The fundamental logical act, the judgment, finds its verbal

154 THE JOURNAL OF PHILOSOPHY

form in the proposition." (2) Logic is concerned with this inner
activity that underlies expression and not with the expression : this
bears the character of something accidental to the thought.

This conception of the field of logic does not prevail with the
unanimity that the volume suggests. It contains two sources of
confusion which have been pressed many times in recent discus-
sion. One of these is that when we choose for the field of logic
thought and not expression we are dealing with a field which is
better left to the psychologists. Thought seems to be a process
in time which occurs whether it is logical or not. Logic does not
pretend to offer causal laws for thought and is so left to furnish
normal laws — but there are grave difficulties in the way of author-
izing these normal laws. Why any one should think "logically"
when thinking illogically will be successful can not be made clear.
To avoid the discussion of empirical thinking logicians are forced
to invent a purely fictitious "rational activity" and to apply to
this the laws of pure thought. The second difficulty is that if we
consider thought as something over and beyond expression, some-
thing that never comes to complete expression, we have for the sub-
ject-matter of logic not merely the not-expressed, but even the non-
expressible. Our data are in a form which can not be discussed,
compared, described or shared.

These difficulties are to be overcome only by a radical change of
attitude. Of all the writers Couturat is least involved in the
course of his paper in problems of "the act of judgment," "pure
rational activity," and like never-expressed, unknowable matters,
and the reason is that his definition of the province of logic is only
a half-hearted concession to a tradition and his real attitude is
more like that of Padoa, whose symbolic logic is frankly an ideogra-
phy with rules for use. In reality Couturat represents this more
modern position which lacks the explicit recognition it deserves in
the volume of the Encyclopedia. When it is formulated it will
include at least the following two provisions: (1) The field of logic
must be redefined as the structure of expression rather than
thought. (2) The meaning of propositions as distinct from the
propositions themselves is not (for logic) an entity independent of
any particular expression, but is a function of the expression,
usually indicating equivalence of two expressions or a possibility
of substitution. The question, "What does this mean?" is not un-
answerable, as it would be if meaning were distinct from expres-
sion, but is answerable by a second expression which can be substi-
tuted for the first. Windleband would have it that "the thought
form as such never comes to expression in speech." His conse-
quent difficulties are beautifully illustrated in his article. "If,"

PSYCHOLOGY AND SCIENTIFIC METHODS 155

he says, "... I say of gold that it possesses the property of yel-
lowness (which is the logical meaning of the proposition that affirms
of the subject 'gold' the predicate 'yellow'), so I may equally well
say of yellow it is a property of gold; but verbally the conversion
of 'gold is yellow' to 'yellow is gold' would appear as incorrect,
or at least not as the exchange of subject and predicate, but only
as an uncommon and inverse form of proposition." He could
hardly have avoided giving verbal expression to the real logical
meaning (which was never to come to expression in speech) and
his choice seems to common sense to be between two differing verbal
expressions rather than between a real meaning not expressed and
a verbal expression. Real meaning must be for logic equivalence
of forms. In fact this is what is actually observed when logicians
pretend to be dealiug with "true meaning." What we are offered
is an equivalent statement. When Bosanquet refers to the "true
meaning" of a statement, he offers us what he would have said or
what might better have been said.

Logic in this sense will not represent the actual play of con-
sciousness by which scientists and common men make additions to
knowledge nor the path which they should follow in order to arrive
at truths, but the structure of expression of truths once found.
Logical laws will represent agreement as to form that must precede
communication, agreement which conditions expression. The "log-
ical act," the judgment, the actual or desirable thought process,
remain a mystery to the psychologist and are barren ground for
logical research. On the other hand, the rules which govern the
expression of thought can be determined from expression. Logic
as a descriptive and a normative science becomes possible. Geome-
tries do not contain histories of the thinking and the motives of
the geometers who discovered their theorems, but a statement of
the theorems connected with the body of the science in certain set
ways. We need not think in syllogisms or any other of the forms
of logic. This was Mr. Schiller's contention in his "Formal Logic"
and is perfectly justified. His error lies in not recognizing that
communication, the sharing and storing of knowledge would be im-
possible except in expression, usually verbal, that is through and
through formal, that possesses a definite structure. In an argu-
ment we do not reproduce our train of imagery in another's mind,
nor need we try. It is sufficient to speak by the card. Discovery
and proof are different matters. Logic deals with the latter, the
former we may leave to psychology with the expectation of little
help. Formulation of the art of thinking is not far advanced.
Windleband's greatest insight is in his admission that "perceiving
and knowing as empirical functions are entirely social in their na-

156 THE JOURNAL OF PHILOSOPHY

ture." Together with his later statement that the normative con-
straint of logic is felt "as soon as an assertion is made" the way
was prepared for better things than the "purely theoretical prin-
ciples," the "pure logic," the "a priori" laws of valid thinking
with which his paper is concerned.

Such discussion of "real meanings" and "pure thought" which
is "never brought to complete expression" comes from two sources.
One of them is the fact of inner speech which is but rehearsed ex-
pression. The other is the desire to attribute the equivalence of
varying expressions, the interchangeability of differing verbal
forms, to an underlying unity of which both are "imitations" or
"signs." There must be one entity which both can "copy." This
motive would require a modern Hume for its complete subjugation.
The "something, I know not what" that underlies expression is a
thing in itself of which the logician may well beware. The dis-
cussible matter of logic seems to be confined to expression, and logic's
task should be rather to examine the forms of expression for their
structure, to invent new and simpler forms, to codify the relations
between forms, even if this means that we surrender that mystical
satisfaction that comes from the discussion of the ineffable — real
meanings that are different from expressed ones.

If this view of logic is the correct one, logic ceases to be the
a priori condition of thought and becomes the a priori condition of
expression, but its a-priority becomes relative to its use, to the group
within which it is established. Logic takes on a human character
very different from the awe-inspiring divine science of order which
Royce presents. We may find logics rather than logic. We can
say no more than that in a certain group a certain structure of ex-
pression prevails, a certain agreement as to the use of language,
and this group need not be defined by differing forms of human
culture, it may be limited by the specialization of a science. The
logic of mathematics consists of agreements in form of statement
that would be entirely unable to deal with the uses of ordinary life.
Not all human expression will submit to the rigid forms of mathe-
matical logic whose limited number and comparatively simple and
abstract character makes them so easily symbolized. Between old
friends a shrug may convey an intricate and definite meaning. The
logic of mathematics does not mention shrugs.

It requires a very delicate metaphysical discrimination to de-
termine the sense in which forms of reasoning are valid for men
who do not use them. A man on a desert island with a companion
dog needs little of the complicated structure of the logistic. A few
simple uniformities which he must observe in calling to his dog
suffice. What else he has will be memories of former association

PSYCHOLOGY AND SCIENTIFIC METHODS 157

with men, or will apply to anticipated meeting with his fellows.
He need make no assertions. His thinking need not have the
structure of logic. He needs no syllogisms with which to avoid a
storm or take nourishment. A feeling of hunger, the sight of food,
motor habits, all the stock of terms granted to the psychologist,
apply to his situation. The logician must concern himself else-
where.

Not only can logic include more than the logic of Aristotle, as
the modern logistic does, there might have been non-Aristotelian
logics with principles different from the familiar laws of contra-
diction and excluded middle. What final authority would judge
between the ultimate "correctness" of Aristotle's logic which offers
two contradictories defined by the axioms : x -f- x' = 1, x — x' = 0.
(x')' = x and a logic which would provide three contradictories as
would the following axioms : x + x'-\- x"= 1, x — x'— x"= 0. (x) '—
x', (x')' = x", (#")' = x% It is true that we can only discuss other
logics in terms of one logic, but this is no more a proof that they
are therefore unreal than is the fact that an Englishman in dis-
cussing German must use Engish, a proof that English is the a
priori condition of communication, valid for all times and all places.
The principles of such logics will not imply the immutability of
the real, but only the comparative immutability of the terms in
which it is discussed, during the discussion.

Not only is there a divergence between the complete logic that
will provide for all intercourse and the limited field to which the
mathematician restricts himself, it is also true that this body of
abstract rules which is susceptible of symbolic statement may be
developed into a calculus and carried to a degree of intricacy that
passes all need for intercourse even between mathematicians. For-
mulas may be constructed that can never serve, or never find in-
stances of use. At this point logistic ceases to be logic and becomes
mere calculus, a branch of mathematics of interest only as a game.
To a certain extent the logistic coincides with the logic of ordinary
intercourse ; for some distance beyond it offers a structure for state-
ment and proof useful to the mathematician only; beyond that it
is a mathematician's amusement. The mathematical treatment of
logic becomes a mistreatment.

The logic of science has pretended to determine how the expan-
sion of scientific knowledge takes place. What it really does is to
exhibit the structure to which new matter must conform to be un-
derstood by other workers, the schemata of expression and com-
munication, not the actual thought processes of investigators. We
can not make chemists by imparting to laymen the logic of science.
We have no successful formulas for discovery and invention. Col-

158 THE JOURNAL OF PHILOSOPHY

lege courses in logic which pretend to impart the ability to think
profitably in various fields of endeavor are a snare and a delusion.
Jevon's four stages of induction, like those of Enriques, and a host
of others, hopelessly confuse two different matters, the thought
process by which a scientist arrives at a discovery, which goes by
very devious ways, and the schema by which he connects his dis-
covery with the body of his science, the schema of proof or demon-
stration. This is rational. The thought process may or may not
be rational. "Rational" and "logical" are best taken to their first
sense in which they apply to verbal expression.

We find ourselves in entire agreement with Russell in his belief
that truth is quite accidental to propositions as far as logic is con-
cerned. Logic is not concerned with the truth or validity of ideas
as Windleband would have us believe; it is rather life itself that
is concerned with their truth and validity, logic with the structure
of discourse and expression.

Edwin Guthrie.
University op Washington.

PURPOSE AND CAUSALITY

IN Part II. of Professor "Warren's "Study of Purpose," 1 we find
the statement that before Darwin's time "the only alternatives
for explaining progress were 'design' and 'chance,' " but that Darwin
himself "pointed out an intermediate alternative in 'natural selec-
tion.' " Later on we read, "if, through some chance variation, a
peripheral organ appears in some creature, which is capable of being
stimulated by the juices emanating from food, the creature possessing
that variation is . . . more likely to survive and have offspring than
the rest of the species."

Is there not a contradiction here ? If the doctrine of natural selec-
tion includes the principle of chance variation, can natural selection
logically be regarded as "an intermediate alternative" between
chance and design ? If variations come by chance, how is this a third
alternative? Does it any more than very partially relieve the "ab-
surdity" to which Dr. Warren refers of attributing all progress to
"mere chance"? Natural selection may explain in a manner satis-
factory to science why certain variations persist and others dis-
appear, but it leaves the problem of the origin of these variations
quite as much in the air as it was before.

But there is a way out of this difficulty if we define the concept of
chance more carefully. The term "chance variations" should not be

i This Journal, Vol. XIII., page 40.